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Abstract and Applied Analysis
Volume 2014, Article ID 720283, 10 pages
http://dx.doi.org/10.1155/2014/720283
Research Article

Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation

1College of Science, China University of Petroleum (East China), Qingdao 266580, China
2Department of Basic Courses, Air Force Aviation University, Changchun, Jilin 130022, China
3School of Mathematics, Jilin University, Changchun, Jilin 130024, China
4School of Business, Northeast Normal University, Changchun, Jilin 130024, China

Received 13 December 2013; Accepted 25 February 2014; Published 3 April 2014

Academic Editor: Jifeng Chu

Copyright © 2014 Haihong Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We analyze a predator prey model with stochastic perturbation. First, we show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. After that, conditions for the system going extinct in probability are established. At last, numerical simulations are carried out to support our results.